- #1
danielhep
- 14
- 1
Homework Statement
A string is wrapped around a uniform solid cylinder of radius r, as shown in (Figure 1) . The cylinder can rotate freely about its axis. The loose end of the string is attached to a block. The block and cylinder each have mass m.
Find the magnitude α of the angular acceleration of the cylinder as the block descends.
Homework Equations
F=ma=mg-T
Torque=Iα=-Tr
a=-rα
I=mr2/2
The Attempt at a Solution
I use these three equations to eliminate T and solve for α.
m(-rα)=mg-T
-1/2mr=T
-mrα=mg+1/2mr
-α=g/r+1/2
α=-1/2-g/r
I tried this answer however it was wrong.
Mastering says the correct answer is
α = 2g/3r
I'm really not sure where this comes from, so any help would be great! I need to understand where I went wrong.